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Section IVSymbols and Higher-Level

Activities

Unit 25Higher-Level Activities and

Concepts

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Algebraic Thinking

• A way of thinking beyond numerical reasoning• Can begin in the elementary grades• Reflected in pre-primary children:

– sorting and grouping objects– combining groups– counting totals– building with blocks– using objects as symbolic representations

• Is supported by science inquiry activities

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Higher Levels of Classification

• Multiple classification

• Inclusion relations

• Hierarchical classification

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Reproducing Shapes

• Done informally– geoboards– pipe cleaners or straws can be left out for

children to use to make shapes

Reproducing Shapes

• Done informally– Geoboards

– pipe cleaners or straws can be left out for children to use to make shapes

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Spatial Relations

• Introduce children to maps

• Begin with a classroom map

• Include maps in the dramatic play area

Spatial Relations

• Introduce children to maps

• Begin with a classroom map

• Include maps in the dramatic play area

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Fourth Level of Graphs

• Introduces the use of squared paper– child colors in squares drawn on a paper

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Concrete Whole Number Operations

• Addition• Subtraction• Multiplication• Division• Requires that child has a basic understanding of

– one-to-one correspondence– number and counting– comparing

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The Symbolic Level

• Connecting groups and symbols in addition and subtraction

• Requires that the child can– connect groups and symbols– identify numerals zero to nine– do concrete addition and subtraction

problems

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Quantities Above Ten

• Require that the child can – count 10 objects correctly– identify numerals 1 to 10– have a good grasp of one-to-one

correspondence– accurately count by rote past 10– move on to counting quantities above 10

Computer Software

• Can be used to explore higher-level concepts and skills